The proof of Lemma REF , uses concentration techniques for matrix valued martingales that were popularized by [1]}, [2]}. By specializing a result like the matrix Friedman inequality of [1]}, we would be able to establish that an inequality like
\(\lambda _{\max }\left( S_{T,i}^{-1} - \tilde{S}_{T,i}^{-1} \ \right) \leqslant c \lambda _{\max }\left( \tilde{S}_{T,i}^{-1} \right) + \log (d/\delta ).\) 
